Solve for x 3(x+4)=5(x-2)

$3 (x + 4) = 5 (x - 2)$

Step 1

Simplify $3 (x + 4)$ .

Rewrite.

$0 + 0 + 3 (x + 4) = 5 (x - 2)$

Simplify by adding zeros.

$3 (x + 4) = 5 (x - 2)$

Apply the distributive property.

$3 x + 3 \cdot 4 = 5 (x - 2)$

Multiply $3$ by $4$ .

$3 x + 12 = 5 (x - 2)$

Step 2

Simplify $5 (x - 2)$ .

Apply the distributive property.

$3 x + 12 = 5 x + 5 \cdot - 2$

Multiply $5$ by $- 2$ .

$3 x + 12 = 5 x - 10$

Step 3

Move all terms containing $x$ to the left side of the equation.

Subtract $5 x$ from both sides of the equation.

$3 x + 12 - 5 x = - 10$

Subtract $5 x$ from $3 x$ .

$- 2 x + 12 = - 10$

Step 4

Move all terms not containing $x$ to the right side of the equation.

Subtract $12$ from both sides of the equation.

$- 2 x = - 10 - 12$

Subtract $12$ from $- 10$ .

$- 2 x = - 22$

Step 5

Divide each term in $- 2 x = - 22$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 22$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 22}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 22}{- 2}$

Divide $x$ by $1$ .

$x = \frac{- 22}{- 2}$

Simplify the right side.

Divide $- 22$ by $- 2$ .

$x = 11$